Question

According to the National Institute on Drug Abuse, a U.S. government agency, 17.3% of 8th graders in 2010 had used marijuana at some point in their lives. A school official hopes to show the percentage is lower in his district, testing H0: p = 0.173 versus Ha: p < 0.173. The health department for the district uses anonymous random sampling and finds that 10% of 80 eighth graders surveyed had used marijuana. Is the sample size condition for conducting a hypothesis test for a population proportion satisfied? No, because 80 students is not enough to be representative of the students in the school district. Yes, because (80)(.173) and (80)(1 ‑ 0.173) are both at least 10. This means we can use the normal distribution to model the distribution of sample proportions. No, because (80)(.10) is less than 10. Because of this the sample size is too small to use the normal distribution to model the distribution of sample proportions. Yes, because the sample is random. It represents the 8th graders in the district.

Answer 1

Answer:

No

Step-by-step explanation:

We have:

n = 80,

p = 0.1  (10%)

q = 1 - p = 1 - 0.1 = 0.9

Usually we use

np > 5, and nq > 5, but this question is using

np > 10, so we'll use that.  It means that the proportion times the sample size must be greater than 10, we have

80(0.1) = 8 and

80(0.9) = 72,

since we got 8 as one answer, the situation doesn't hold up.